function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

predictions = sigmoid(X*theta);	% predictions of hypothesis on all m
errors = -y .* log(predictions) - (1-y) .* log(1-predictions); % errors
regTerm = lambda/(2*m) * sum(theta(2:size(theta)).^2); % regularization term
J = 1/m * sum(errors) + regTerm;

grad = 1/m .* X' * (predictions - y);
temp = theta; 
temp(1) = 0;   % because we don't add anything for j = 0
grad = grad + lambda / m * temp;




% =============================================================

end
